Syllogism
About 7 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 519 words at 150 words a minute, plus a minute for each question.
It tests your ability to draw logical conclusions from two given statements using categorical quantifiers: "All," "Some," and "No." Unlike other reasoning topics that require spatial or verbal tricks, syllogism follows strict logical rules.
Key ideas
- Categorical statements: Syllogism uses four types—Universal Affirmative (All A are B), Universal Negative (No A are B), Particular Affirmative (Some A are B), and Particular Negative (Some A are not B). Each has a distinct logical meaning.
- Venn diagram method: Represent each statement as overlapping or separate circles. "All A are B" means circle A lies entirely inside B. "No A are B" means circles A and B do not touch. "Some A are B" means circles overlap partially. This visual method eliminates guesswork.
- Complementary pairs: "All" and "Some not" are complements; "No" and "Some" are complements. If "All dogs are animals" is false, then "Some dogs are not animals" must be true. Recognizing these pairs helps in either-or conclusions.
- Follow from statements, not reality: Even if a statement seems illogical ("All books are trees"), treat it as true for that problem. The exam tests deductive logic, not general knowledge.
- "Some" means at least one: In logic, "Some A are B" means one or more A belong to B. It does not mean "only a few" or "not all." This precise interpretation is crucial.
Watch out for
- Using real-world logic: Students reject "All chairs are dogs" as absurd and refuse to draw it. In syllogism, accept every statement as given. Evaluate only logical deduction, not real-world truth.
- Assuming "Some" means "not all": In everyday language, "some" often implies "not all." In formal logic, "Some A are B" allows for the possibility that all A are B. Do not add restrictions the statement does not contain.
- Ignoring Venn overlaps: Drawing sloppy or no diagrams leads to guessing. A statement can allow more than one Venn arrangement (e.g., "Some A are B" also allows all of A inside B), so check them all.
Quick reference
- All A → B: A circle fully inside B circle.
- No A ↔ B: A and B circles separate, no overlap.
- Some A ∩ B: A and B circles overlap partially.
- "All A are B" ⇒ "Some B are A" (but NOT "All B are A").
- "No A are B" ⇔ "No B are A" (symmetric).
Check yourself: 3 questions
1. Statements: All books are pages. All pages are papers. Conclusions: I. All books are papers. II. Some papers are books. Which conclusion(s) logically follow(s)?
2. Statements: Some pens are pencils. No pencil is an eraser. Conclusions: I. Some pens are not erasers. II. No pen is an eraser. Which conclusion(s) logically follow(s)?
3. Statements: All chairs are tables. Some tables are desks. No desk is a bench. Conclusions: I. Some chairs are desks. II. No bench is a table. Which conclusion(s) logically follow(s)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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